I need to throw this in the mix.
As Blade - I think - was trying to point out, hospital births with midwives are the "lowest" in risk not only because of the midwives skill level but also their proximity to emergancy care. The same midwife-group in a home setting could end-up with very different statistics should emergancy care for mother and child be 5 minutes away.
The idea is that if you are having an uncomplicated birth it doesn't really matter where you are.
However, should their be a complication or emergancy situation you and your child are statistically better off in a hospital which is equipped to handle such emergencies. (Also something important to consider when doing research early on).
The reason why the hospital-midwife statistics are lowest isn't necessarily that they are the "best" but because they only get the numbers for the uncomplicated hospital-births while high-risk pregnancies and complications are immediately transferred to a doctor. (So obviously the doctors numbers are skewed because they include almost all of the hospitals high-risk pregnancies).

Yes, these are American statistics but the general findings probably don't change much (at least for hospital-midwives vs hospital-doctors) in any country with a comparable medical-skill level). This has nothing to do with who the midwife is but purely what location the baby is born in. Saying that home-births in New Zealand or Australia are "safer" because it's the same midwife as in the hospital is fallacious. It may very well be the case that they are better trained and have higher professional requirements (which is always awesome), but you can't compare personal numbers to location numbers -> it's like comparing apples and celery.

Interesting post! I am not very good with all the numbers/statistics but reading your final statement helped keep me in the mind set of why I want to have my first child and all children probably in a hospital with the professionals. I know two people who had their first child at home and it totally freaks me out. Granite it went well for them. But my thoughts are, do they know what they are truly doing (midwives)? Do they have machines monitoring my baby, and what if something where to go wrong how much of a window period do you truly have to rush yourself and your baby to a hospital? Too many risky factors with a home birth to ever do it. Great article Blade!

Very important research! I am really glad someone did an extensive study on this. Personally, I've always felt much safer in a hospital than most people probably do (had a parent in healthcare) so I'm gratified to hear that the birth setting I've used is probably the safest.

My only question is, from my limited memory of stats, what about the sample size of 14,000 observations? Is that "large" enough to cause issues with p-values and goodness of fit?

I'm not super experienced with big data sets, just genuinely curious about how the info would be interpreted, since I will eventually be doing a research project for my masters.